Organizing and accessing contact information in Outlook.com
To the best of my knowledge, you cannot sync iCloud with Outlook.com (a Microsoft mailbox accessed with a web browser). You can, however, export the contacts from iCloud to a vcf file, then convert that file to a csv format file, which you can then import into Outlook.com. If you were to update the iCloud contacts, you'd have to make the same changes in Outlook.com or import the entire list again.
That said, you can sync the iPhone contacts to an Outlook.com mailbox if you use the Outlook for iOS app. That's fairly straightforward.